This invention relates to methods for calculating the in-plane fracture toughness of a thin film formed on a substrate.
Thin films are very important in many applications. For example, thin films are used extensively in microelectronics applications where devices often have features of submicron size. Thin films are also used extensively in micro-mechanical applications for making devices such as microgears and accelerometers, and other applications such as for making hard disks in a hard drive and hard coating for gear boxes.
Determining the mechanical properties of thin films in these applications can be of critical importance. For example, a thin film having a large tensile stress may delaminate, causing device failure under certain conditions. The mechanical properties of a thin film material cannot simply be predicted based upon the properties of the bulk material for a number of reasons. First, the mechanical properties of the thin film generally differ from that material in its bulk form based on factors such as the particular technique for forming the film, and the conditions under which the film is formed. For example, a thin film formed on a substrate at high temperature and then cooled to room temperature may exhibit either a tensile or compressive stress due to the difference in the coefficient of thermal expansion between the film and the substrate.
Also, the underlying substrate in many applications will not have a surface that is smooth or of uniform composition. Instead, the substrate may have features with a varying topography due to thin film layers which are already formed and patterned. The mechanical properties of the thin film may vary across the surface of the film, depending upon both the thin film formation technique and the structure of the underlying substrate. Therefore, techniques for measuring the mechanical properties of thin films that can measure the properties of a small (often submicron) region are desired.
One technique for measuring certain mechanical properties of materials on a small scale uses load-displacement data from a load and displacement sensing system. An example of such a system is shown in FIG. 1. Typically, in such a system, an indenter with a small cross-section is applied to the surface of the material. This type of measurement technique is generally referred to as a microindentation or nanoindentation technique.
In a nanoindentation measurement, a load is applied to the indenter to force it into the material. As the indenter is forced into the material, the amount that the indenter is displaced into the material is measured. Concurrently with the measurement of the indenter displacement, the load applied to the indenter is measured. In general, for a relatively stiff material, the load increase will be greater for a given increase in indenter penetration (displacement) than for a less stiff material.
Because the indenter cross-section can be made quite small, a small area of a thin film may be probed. The mechanical properties of the thin film may therefore be mapped with submicron resolution. This is important for applications where the mechanical properties of the thin film may be expected to vary over a short distance across the surface of the film, such as when the underlying substrate has topological features of submicron size. The submicron resolution of nanoindentation techniques allows problem regions of the thin film to be identified, and potentially the problems in those regions may then be solved by adjusting the thin film deposition parameters, and/or the structure of the underlying substrate.
In a typical load and displacement measurement, the load on the indenter is increased to a maximum value, and then the load is decreased until the indenter is free from the material. Often at higher maximum loads, the material will remain deformed upon releasing the load on the indenter. A typical load/displacement behavior is shown in FIG. 2.
Using load-displacement data from a system similar to that of FIG. 1, Oliver and Pharr calculated the elastic modulus and hardness of bulk materials such as sapphire, quartz, tungsten, and aluminum, "An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments", J. Mater. Res., Vol. 7, No. 6, June 1992, pp. 1564-1583. However, unlike bulk materials, thin films have the added complication of an underlying substrate. When forcing an indenter into a thin film, not only will the thin film deform, but the substrate will deform as well. Therefore, calculation of the mechanical properties of a thin film involves taking into account the mechanical properties of the underlying substrate as well.
It is also known to measure certain mechanical properties of thin films using a nanoindentation technique. For example, Tsui et al. calculated the hardness of soft-film/hard-substrate systems such as Al/Glass, Al/ALON, and Al/sapphire in "Effects of Adhesion on the Measurement of Thin Film Mechanical Properties by Nanoindentation", Mat. Res. Soc. Symp. Proc. Vol. 473, March 31-April 3, 1997, pp. 51-56, while Doerner et al. investigated the strength of aluminum and tungsten films in "Plastic properties of thin films on substrates as measured by submicron indentation hardness and substrate curvature techniques", J. Mater. Res., Vol. 1, No. 6, November/December 1986, pp. 845-851 (1987). While there exist techniques for measuring certain mechanical properties of thin films, such as hardness and the elastic modulus, using a load and displacement sensing system, such techniques cannot be readily be applied to measure the in-plane fracture toughness of the thin film. Therefore, there exists a need for reliably and effectively measuring the in-plane fracture toughness, .kappa., of a thin film formed on a substrate using nanoindentation techniques.